Where can I get a list of inversely and directly related futures markets and their correlations to each other?
MRCI is OK at first but in many respects it is quite limited - try out CSI or find someone with a Bloomberg terminal if you really want to dig into this. And "lists" change all the time - especially if currencies are involved and some "not so obvious" futures intermarket combinations.
Ask for a free trial for the correlation lab. You'll find it much more capable than MRCI and a hell of a lot cheaper than a Bloomberg terminal.